Load an image from URL as base64 string

It seems to me that you need to separate the base64 part, which is only needed in your HTML, from fetching the data from the response. Just fetch the data from the URL as binary data and convert that to base64. Using HttpClient makes this simple:

public async static Task<string> GetImageAsBase64Url(string url)
{
    var credentials = new NetworkCredential(user, pw);
    using (var handler = new HttpClientHandler { Credentials = credentials })
    using (var client = new HttpClient(handler))
    {
        var bytes = await client.GetByteArrayAsync(url);
        return "image/jpeg;base64," + Convert.ToBase64String(bytes);
    }
}

This assumes the image always will be a JPEG. If it could sometimes be a different content type, you may well want to fetch the response as an HttpResponse and use that to propagate the content type.

I suspect you may want to add caching here as well :)